The maximum number of S_{r-1,k}^r copies in an r-uniform hypergraph with matching number at most ν is independent of k and equals the number in the extremal construction given by the Erdős Matching Conjecture; this implies the conjecture holds in the (r-1,k)-norm for all k.
Nondegenerate Turán problems under(t, p)-norms.arXiv preprint arXiv:2406.15934, 2024
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Confirms uniqueness of balanced bipartite extremal for ℓ₂ Turán on K₅³ and exact clique count in K₅³-free 3-graphs for large n via vertex-colored Turán theorems and local modifications.
Determines the maximum number of t-cliques in n-vertex r-graphs with bounded (j,p)-norm when p>(t-j)/(r-j), proved via entropy plus interpolation and sharp for Steiner systems.
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Counting sunflowers in hypergraphs with bounded matching number and Erd\H{o}s Matching Conjecture in the $(t,k)$-norm
The maximum number of S_{r-1,k}^r copies in an r-uniform hypergraph with matching number at most ν is independent of k and equals the number in the extremal construction given by the Erdős Matching Conjecture; this implies the conjecture holds in the (r-1,k)-norm for all k.
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Vertex-colored Tur\'{a}n theorems with applications in extremal hypergraph problems
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